Invertibility of causal discrete time dynamical systems

Abstract

AbstractWe show that a causal discrete time dynamical system, which is represented by a difference equation, can be written as x(t)=F(x(t-1)), where the Jacobian matrix ∂F/∂x is non-singular. This invertibility or reversibility property, which is the analogue of the one-parameter group associated with a dynamical system represented by an ordinary differential equation, is obtained via techniques resulting from difference algebra